Aspects of line-fitting in bivariate allometric analyses

One of the fundamental problems involved in analyses of the scaling effects of body size (allometric analysis is the choice of an appropriate best-fit line in bivariate logarithmic plots. Following a discussion of some basic aspects of allometric analysis, the tow mai procedures for the determination of a best-fit line - the least-squares regression and the major axis - are examined with respect to their different properties and underlying models. It is important to distinguish intraspecific from interspecific scaling and to recognize the distinction between use of a best-fit line to define a relationship and use of the line for prediction. An alternative model to the bivariate normal distribution, referred to as the 'extruded normal distribution', is presented and its implications are examined with respect to two test cases (scaling of basal metabolic rate in human males; scaling of population density in mammals).     

Pharmacokinetic allometric scaling of oligonucleotides

The objective of this study was to evaluate the predictive performance of interspecies scaling of oligonucleotides to predict clearance and volume of distribution at steady state in humans from animal data. The human pharmacokinetic parameters were predicted using 1, 2, or at least 3 animal species. The results of the study indicated that the pharmacokinetic parameters of oligonucleotides can be predicted with reasonable accuracy in humans when at least 3 animal species are employed. On the other hand, allometric scaling based on 1 or 2 species or fixed coefficient or fixed exponent can be erratic and unreliable. Further work should be conducted in this direction.     

Principal components for allometric analysis

Logarithmic bivariate regression slopes and logarithmic principal component coefficient ratios are two methods for estimating allometry coefficients corresponding to a in the classic power formula Y = BXa. Both techniques depend on high correlation between variables. Interpretation is logically limited to the variables included in analysis. Principal components analysis depends also on relatively uniform intercorrelations; given this, it serves satisfactorily as a method for summarizing many bivariate combinations. Unmodified major principal component coefficients cannot represent scaling to body weight; rather, they represent scaling to a composite size vector which usually is highly correlated with body size or weight but has an unspecified allometry. Thus, the concepts of proportionality and of isometry must be kept distinct.     

Exponential growth and allometric equations

Earlier the simple exponential growth law has been used when attempts have been made to explain theoretically the existence of allometric equations in biology (Bertalanffy, 1968; Giinther, 1975). We show here that the exponential growth law in which the proportion coefficient also depends on time is a better approximation. We consider especially the metabolic rate and the body mass of man during the growth process.     

Ecological and behavioral correlates of coloration in artiodactyls: systematic analyses of conventional hypotheses

To test the generality of adaptive explanations for coat colorationin even-toed ungulates, we examined the literature for hypothesesthat have been proposed for color patterns exhibited by thistaxon, and we derived a series of predictions from each hypothesis.Next, we collected information on the color, behavioral, andecological characteristics of 200 species of even-toed ungulatesand coded this in binary format. We then applied chi-squareor Fisher's Exact probability tests that pitted presence ofa color trait against presence of an ecological or behavioralvariable for cervids, bovids, and all artiodactyls. Finally,we reanalyzed the data by using concentrated-changes tests anda composite molecular and taxonomic phylogeny. Hinging our findingson whether associations persisted after controlling for sharedancestry, we found strong support for hypotheses suggestingeven-toed ungulates turn lighter in winter to aid in concealmentor perhaps thermoregulation, striped coats in adults and spottedpelage in young act as camouflage, side bands and dark facesassist in communication, and dark pelage coloration is mostcommon in species living in the tropics (Gloger's rule). Whereaswhite faces, dark legs, white legs, dark tails, and white tailsdid not appear to assist in communication alone, legs and tailsthat were either dark or white (i.e., conspicuous) did seemto be linked with communication. There was moderate supportfor hypotheses that countershading aids concealment, that whitefaces are a thermoregulatory device, and that white rumps areused in intraspecific communication. There was weak supportfor spots in adults and stripes in young providing camouflageand for dark leg markings being a form of disruptive coloration.We found little or no evidence that overall coat color servesas background matching, that side bands are disruptive colorationdevices, or that white rumps help in thermoregulation. Concealmentappears the principal force driving the evolution of colorationin ungulates with communication, and then thermoregulation,playing less of a role.     

Testing the allometric scaling laws

Allometric scaling laws have received increasing attention due to the recent theoretical advancements. However, existing evidence suggests that the scaling relationships may vary a lot without much consistency, which poses a challenge to the applicability of general theories. In this report, I demonstrate that much of the discrepancy may be an artefact caused by the limited use of methods for estimating the parameters in the allometric scaling equations. I suggest alternative procedures that can be utilized to avoid biased interpretations. The comments are largely applicable to any research that involves parameterization of equations.     

On the allometric growth of tissues in fruits

This paper deals with the relative growth of three different fruit tissues. Their morphogenetic periods and the mathematical constraints involved are described, and more precisely, the paper shows an allometric relationship (Y=nX ^m ) between the widths (X, Y) of the main tissues in stone fruits such as cherries, peaches and prunes. The mathematical relationships between the growth of the mesocarp and of the endocarp of somePrunus fruits are described, and it is proved that before the formation of the embryo, growth is allometric, in agreement with conclusions drawn from some experimental data. However, according to another study, the growth of the mesocarp and of the endocarp are ruled by autocatalytic and monomolecular functions, before as well as after the formation of the embryo. In this case, it is proved that if allometry exits in stone fruits, it can only be anantiometry (m=−1). To solve the dilemma, two main alternatives are proposed and discussed. We conclude that, while allometry is established on reasonable grounds before the formation of the embryo, after the formation of the embryo the mesocarp and endocarp evolve independently since a center for the coordination of growth no longer exists, and each tissue can grow according to its own independent rules.     

Comparison of automatic and conventional physical and chemical analyses in Lake Saimaa,Eastern Finland

Hydrobiologia - The Saimaa lake complex (4460&;nbsp;km2) is a mosaic of interconnected basins draining into the Gulf of Finland via Lake Ladoga. Limnologically, most of the basins are...     

异速生长模型研究概述

最近,关于异速生长模型的讨论再次成为焦点,讨论热点为异速生长指数的取值及其理论解释.本文综述了WBE 97、BMR(99)模型的相关研究,重点介绍了MGL模型及由此模型得到的结果:个体整体的新陈代谢率与个体的质量没有明显依赖关系,其标度指数不是一个固定的值,而是一个区间[2/3,1].考虑的视角从个体整体的新陈代谢率转到单位质量的新陈代谢率,通过对不同物种、不同环境的单位质量新陈代谢率的研究,发现对大多数物种,其值落在一个具有普适性的上、下界的区间内;认为存在单位质量的新陈代谢率最小值确定了个体的大小,并建立基于该最小值的描述个体大小与温度关系的数学模型,该模型得到实验数据验证.     

The origin of allometric scaling laws in biology

The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon-specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.     

Genetic mapping of allometric scaling laws

Many biological processes, from cellular metabolism to population dynamics, are characterized by particular allometric scaling relationships between rate and size (power laws). A statistical model for mapping specific quantitative trait loci (QTLs) that are responsible for allometric scaling laws has been developed. We present an improved model for allometric mapping of QTLs based on a more general allometry equation. This improved model includes two steps: (1) use model II regression analysis to estimate the parameters underlying universal allometric scaling laws, and (2) substitute the estimated allometric parameters in the mixture-based mapping model to obtain the estimation of QTL position and effects. This model has been validated by a real example for a mouse F2 progeny, in which two QTLs were detected on different chromosomes that determine the allometric relationship between growth rate and body weight.     

Techniques for estimating allometric equations.

Morphologists have long been aware that differential size relationships of variables can be fo great value when studying shape. Allometric patterns have been the basis of many interpretations of adaptations, biomechanisms, and taxonomies. It is of importance that the parameters of the allometric equation be as accurate estimates as possible since they are so commonly used in such interpretations. Since the error term may come into the allometric relation either exponentially or additively, there are at least two methods of estimating the parameters of the allometric equation. That most commonly used assumes exponentiality of the error term, and operates by forming a linear function by a logarithmic transformation and then solving by the method of ordinary least squares. On the other hand, if the rrror term comes into the equation in an additive way, a nonlinear method may be used, searching the parameter space for those parameters which minimize the sum of squared residuals. Study of data on body weight and metabolism in birds explores the issues involved in discriminating between the two models by working through a specific example and shows that these two methods of estimation can yield highly different results. Not only minimizing the sum of squared residuals, but also the distribution and randomness of the residuals must be considered in determing which model more precisely estimates the parameters. In general there is no a priori way to tell which model will be best. Given the importance often attached to the parameter estimates, it may be well worth considerable effort to find which method of solution is appropriate for a given set of data.     

Model selection and logarithmic transformation in allometric analysis

The standard approach to most allometric research is to gather data on a biological function and a measure of body size, convert the data to logarithms, display the new values in a bivariate plot, and then fit a straight line to the transformations by the method of least squares. The slope of the fitted line provides an estimate for the allometric (or scaling) exponent, which often is interpreted in the context of underlying principles of structural and functional design. However, interpretations of this sort are based on the implicit assumption that the original data conform with a power function having an intercept of 0 on a plot with arithmetic coordinates. Whenever this assumption is not satisfied, the resulting estimate for the allometric exponent may be seriously biased and misleading. The problem of identifying an appropriate function is compounded by the logarithmic transformations, which alter the relationship between the original variables and frequently conceal the presence of outliers having an undue influence on properties of the fitted equation, including the estimate for the allometric exponent. Much of the current controversy in allometric research probably can be traced to substantive biases introduced by investigators who followed standard practice. We illustrate such biases with examples taken from the literature and outline a general methodology by which the biases can be minimized in future research.     

The allometric approach to species differences in brain size

Allometric methods can be used to test quantitative theories of the relationship between brain size and body size across species, and to search for ecological, behavioural, life history, and ontogenetic correlates of brain size. Brain size scales with an allometric exponent of around 0.75 against body size across mammals, but is closer to 0.56 for birds and for reptiles. The slope of the allometric line often varies depending upon the taxonomic level of analysis. However, this phenomenon, at least in mammals, may be a statistical artifact. Brain size for a given body size (relative brain size) varies among orders in birds and mammals, and some dietary associations with relative brain size have been found in particular taxa. Developmental status at birth is the most consistent correlate of relative brain size: precocial neonates have larger brains for a given maternal size than altricial neonates in both birds and mammals. Altricial neonates, however, have more brain growth following birth, and in birds also have larger relative adult brain sizes. Energetic explanations for differences in neonatal brain growth, although attractive on theoretical grounds, have largely failed to stand up to empirical tests.     

Biomechanics and allometric scaling in primate locomotion and morphology

Body size has a dominant influence on locomotor performance and the morphology of the locomotor apparatus. In locomotion under the influence of gravity, body mass acts as weight force and is a mechanical variable. Accordingly, the application of biomechanical principles and methods allows a functional understanding of scaling effects in locomotion. This is demonstrated here using leaping primates as an example. With increasing body size, the decreasing ratio of muscle force available for acceleration during takeoff to the body mass that has to be accelerated dictates both the movement pattern and the proportions of the hindlimbs. In an arm-swinging movement, the long, heavy arms of the large-bodied leapers are effectively used to gain additional momentum. A new perspective on decreasing size identifies the absolutely small acceleration distance and time available for propulsion as factors limiting leaping distance and extensively determining locomotor behavior and body proportions. As the mechanical constraints differ according to body size for a given mode of locomotion, a typological approach to morphology in relation to locomotor category is ruled out. Across locomotor categories, dynamic similarity (sensu Alexander) can be expected if the propulsive mechanisms as well as the selective pressures acting upon locomotion are the same.     

The allometric interpretation of the self-thinning rule

Plant populations growing at high densities undergo density-dependent mortality or self-thinning. The density of survivors ({ρ}) is related to their mean biomass (w) by the power equation w = K_ρ^?a, where a is $\text{3}\text{2}$. This is known as the “self-thinning rule”. This relationship is very general for plant populations and represents both an asymptotic time-trajectory for a particular population and a boundary line for juxtaposed joint values of w and p of separate populations. The traditional allometric derivation of the rule is outlined and shown to be unrealistic. An attempt to reformulate the self-thinning rule, based on the traditional allometric derivation, is shown to be unsatisfactory and an alternative allometric derivation is presented. The rule in its traditional statement $\text{w = K}{}_{\mathrm{\rho }}{}^{\mathrm{?3}}\text{2}$ is still its best expression. The nature of the constant K is discussed with particular reference to its dimensionality.